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# exam3 - must swim from point P to point Q at a rate of 100...

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Exam 3 M170-003 Fall, 2006 Name: (1 pt.) Show all your work. 1. (20 pts.) For f ( x ) = x 3 - x 2 - x fnd: (a) The exact intervals on which f is increasing and the exact intervals on which it is de- creasing. (b) The x - and y -coordinates o± all critical points. Then sketch a graph o± f that agrees with all o± your answers above. Use the graph paper on the next page. 1

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2. (15 pts.) For g ( x ) = 4 sin x + x 2 , with 0 x π , fnd the exact intervals on which g is concave up and those on which it is concave down. 3

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3. (15 pts.) If C ( x ) = 100 xe - x/ 100 + 50 x , use diFerentials to approximate C (100) - C (97). 4. (15 pts.) ±ind lim x π/ 2 (2 x - π ) 2 1 - sin x 4
5. (20 pts.) You need to get from point P to point R as shown in the Fgure at right. You

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Unformatted text preview: must swim from point P to point Q at a rate of 100 ft/min. You then walk from point Q to point R at a rate of 200 ft/min. What is the shortest amount of time it takes to get from P to R ? ±or full credit on this problem you must: (a) Clearly identify a quantity to maximize or minimize. (b) Graph it. (c) Locate extrema exactly and show all work in doing so. Calculator approxima-tions will not receive credit. 350 ft 150 ft P Q R 5 6. (15 pts.) The fgure at right is the graph oF y = 1 + x cos p πx 3 P together with its tangent line at x = 3. ±ind where the tangent line crosses the x-axis. 3 6...
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exam3 - must swim from point P to point Q at a rate of 100...

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